{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/98272"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/98272","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Symmetry-protected topological phases and quantum anomalies","abstract":"We present the correspondence between symmetry-protected topological (SPT) phases and their anomalous boundary states, based on examples in various spacetime dimensions. Through the study of the effect of interactions on these SPT phases, we discovered a new formalism of quantum anomalies, associated with discrete spacetime (such as time-reversal and spatial reflection) symmetries in particular, to classify distinct interacting topological phases. An example is the Z2 classification of the (2+1)d topological insulator protected by charge U(1) and time-reversal (or CP) symmetries, which can be deduced by the form of the global U(1) gauge anomalies on its edge theories defined on closed unorientable manifolds. In this case, the nontrivial phase (in free systems) is robust against electron interactions. Another example is the (3+1)d topological superconductor protected by only time-reversal or reflection symmetry. For this system, we identified the bulk phase by studying the global gravitational anomalies of the surface theories formulated on unorientable spacetime manifolds, and also discussed its connection to the collapse of the non-interacting classification by an integer Z to Z16, in the presence of interactions. We also revisit the problem of gauging a discrete internal symmetry in theories of chiral (Weyl) fermions in 3+1 dimensions – which have not been fully understood so far – from the perspective of fermionic SPT phases in 4+1 dimensions. Comparing with the previous results, we give a complete answer for the anomalies constraints on the discrete symmetry, as our approach is based on purely geometrical considerations, namely, our assumption is more fundamental and general. Furthermore, our result also provides an understanding of gapped states of fermions with anomalous discrete symmetries, and we present a model, based on weak coupling, for constructing these anomalous gapped states.","abstract_html":"We present the correspondence between symmetry-protected topological (SPT) phases and their anomalous boundary states, based on examples in various spacetime dimensions. Through the study of the effect of interactions on these SPT phases, we discovered a new formalism of quantum anomalies, associated with discrete spacetime (such as time-reversal and spatial reflection) symmetries in particular, to classify distinct interacting topological phases. An example is the Z2 classification of the (2+1)d topological insulator protected by charge U(1) and time-reversal (or CP) symmetries, which can be deduced by the form of the global U(1) gauge anomalies on its edge theories defined on closed unorientable manifolds. In this case, the nontrivial phase (in free systems) is robust against electron interactions. Another example is the (3+1)d topological superconductor protected by only time-reversal or reflection symmetry. For this system, we identified the bulk phase by studying the global gravitational anomalies of the surface theories formulated on unorientable spacetime manifolds, and also discussed its connection to the collapse of the non-interacting classification by an integer Z to Z16, in the presence of interactions. We also revisit the problem of gauging a discrete internal symmetry in theories of chiral (Weyl) fermions in 3+1 dimensions – which have not been fully understood so far – from the perspective of fermionic SPT phases in 4+1 dimensions. Comparing with the previous results, we give a complete answer for the anomalies constraints on the discrete symmetry, as our approach is based on purely geometrical considerations, namely, our assumption is more fundamental and general. Furthermore, our result also provides an understanding of gapped states of fermions with anomalous discrete symmetries, and we present a model, based on weak coupling, for constructing these anomalous gapped states.","abstract_has_math":false,"creators":["Hsieh, Chang-Tse"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Ryu, Shinsei","Stone, Michael","Leigh, Robert G.","Eckstein, James N."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-09-29T16:39:42Z","date_published":"2017-09-29T16:39:42Z","updated_at":"2026-07-22T22:24:35Z","subjects":["Symmetry-protected topological phases","Topological insulators and superconductors","Classification","Strongly correlated systems","Quantum anomalies","Orientifold conformal field theories","Discrete gauge anomalies","'t Hooft anomalies"],"languages":["en"],"rights":["Copyright 2017 Chang-Tse Hsieh"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/98272","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ryu, Shinsei","Stone, Michael","Leigh, Robert G.","Eckstein, James N."]},{"key":"dc:creator","label":"Author","values":["Hsieh, Chang-Tse"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-09-29T16:39:42Z","2019-09-30T09:15:29Z","2017-07-11","2017-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Symmetry-protected topological phases","Topological insulators and superconductors","Classification","Strongly correlated systems","Quantum anomalies","Orientifold conformal field theories","Discrete gauge anomalies","'t Hooft anomalies"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Chang-Tse Hsieh"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/98272"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We present the correspondence between symmetry-protected topological (SPT) phases and their anomalous boundary states, based on examples in various spacetime dimensions. Through the study of the effect of interactions on these SPT phases, we discovered a new formalism of quantum anomalies, associated with discrete spacetime (such as time-reversal and spatial reflection) symmetries in particular, to classify distinct interacting topological phases. An example is the Z2 classification of the (2+1)d topological insulator protected by charge U(1) and time-reversal (or CP) symmetries, which can be deduced by the form of the global U(1) gauge anomalies on its edge theories defined on closed unorientable manifolds. In this case, the nontrivial phase (in free systems) is robust against electron interactions. Another example is the (3+1)d topological superconductor protected by only time-reversal or reflection symmetry. For this system, we identified the bulk phase by studying the global gravitational anomalies of the surface theories formulated on unorientable spacetime manifolds, and also discussed its connection to the collapse of the non-interacting classification by an integer Z to Z16, in the presence of interactions. We also revisit the problem of gauging a discrete internal symmetry in theories of chiral (Weyl) fermions in 3+1 dimensions – which have not been fully understood so far – from the perspective of fermionic SPT phases in 4+1 dimensions. Comparing with the previous results, we give a complete answer for the anomalies constraints on the discrete symmetry, as our approach is based on purely geometrical considerations, namely, our assumption is more fundamental and general. Furthermore, our result also provides an understanding of gapped states of fermions with anomalous discrete symmetries, and we present a model, based on weak coupling, for constructing these anomalous gapped states.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-08-01","The student, Chang-Tse Hsieh, accepted the attached license on 2017-07-11 at 09:49.","The student, Chang-Tse Hsieh, submitted this Dissertation for approval on 2017-07-11 at 10:21.","This Dissertation was approved for publication on 2017-07-11 at 15:28.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11392 on 2017-09-29 at 11:18:28","Made available in DSpace on 2017-09-29T16:39:42Z (GMT). No. of bitstreams: 3 HSIEH-DISSERTATION-2017.pdf: 1199945 bytes, checksum: 7a3bc459e20089847aea925726fc38dc (MD5) LICENSE.txt: 4212 bytes, checksum: f06fde22d36371936a11d08b60a0eebd (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: b86adde1710a60c3e8e0403b5766dd2c (MD5) Previous issue date: 2017-07-11","Embargo set by: Colleen Fallaw for item 103419 Lift date: 2019-09-29T16:39:52Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Colleen Fallaw for item 103419 Lift date: 2019-09-29T17:52:45Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 103419 on 2019-09-30T09:15:29Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Symmetry-protected topological phases and quantum anomalies"]}]}],"canonical_facts":{"dc:contributor":["Ryu, Shinsei","Stone, Michael","Leigh, Robert G.","Eckstein, James N."],"dc:creator":["Hsieh, Chang-Tse"],"dc:date":["2017-09-29T16:39:42Z","2019-09-30T09:15:29Z","2017-07-11","2017-08"],"dc:description":["We present the correspondence between symmetry-protected topological (SPT) phases and their anomalous boundary states, based on examples in various spacetime dimensions. Through the study of the effect of interactions on these SPT phases, we discovered a new formalism of quantum anomalies, associated with discrete spacetime (such as time-reversal and spatial reflection) symmetries in particular, to classify distinct interacting topological phases. An example is the Z2 classification of the (2+1)d topological insulator protected by charge U(1) and time-reversal (or CP) symmetries, which can be deduced by the form of the global U(1) gauge anomalies on its edge theories defined on closed unorientable manifolds. In this case, the nontrivial phase (in free systems) is robust against electron interactions. Another example is the (3+1)d topological superconductor protected by only time-reversal or reflection symmetry. For this system, we identified the bulk phase by studying the global gravitational anomalies of the surface theories formulated on unorientable spacetime manifolds, and also discussed its connection to the collapse of the non-interacting classification by an integer Z to Z16, in the presence of interactions. We also revisit the problem of gauging a discrete internal symmetry in theories of chiral (Weyl) fermions in 3+1 dimensions – which have not been fully understood so far – from the perspective of fermionic SPT phases in 4+1 dimensions. Comparing with the previous results, we give a complete answer for the anomalies constraints on the discrete symmetry, as our approach is based on purely geometrical considerations, namely, our assumption is more fundamental and general. Furthermore, our result also provides an understanding of gapped states of fermions with anomalous discrete symmetries, and we present a model, based on weak coupling, for constructing these anomalous gapped states.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-08-01","The student, Chang-Tse Hsieh, accepted the attached license on 2017-07-11 at 09:49.","The student, Chang-Tse Hsieh, submitted this Dissertation for approval on 2017-07-11 at 10:21.","This Dissertation was approved for publication on 2017-07-11 at 15:28.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11392 on 2017-09-29 at 11:18:28","Made available in DSpace on 2017-09-29T16:39:42Z (GMT). No. of bitstreams: 3 HSIEH-DISSERTATION-2017.pdf: 1199945 bytes, checksum: 7a3bc459e20089847aea925726fc38dc (MD5) LICENSE.txt: 4212 bytes, checksum: f06fde22d36371936a11d08b60a0eebd (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: b86adde1710a60c3e8e0403b5766dd2c (MD5) Previous issue date: 2017-07-11","Embargo set by: Colleen Fallaw for item 103419 Lift date: 2019-09-29T16:39:52Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Colleen Fallaw for item 103419 Lift date: 2019-09-29T17:52:45Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 103419 on 2019-09-30T09:15:29Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/98272"],"dc:language":["en"],"dc:rights":["Copyright 2017 Chang-Tse Hsieh"],"dc:subject":["Symmetry-protected topological phases","Topological insulators and superconductors","Classification","Strongly correlated systems","Quantum anomalies","Orientifold conformal field theories","Discrete gauge anomalies","'t Hooft anomalies"],"dc:title":["Symmetry-protected topological phases and quantum anomalies"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:35Z"}